Scaling properties of a non-Fowler-Nordheim tunneling junction

Recent experimental work [1] has shown that there is a simple scaling function for the current I in a sharp tunneling junction as a function of the tip anode distance d. When the emitter has a large radius of curvature R the tunneling potential depends linearly on the field and scaling the latter with d obviously leads to the scaling of the current. But when the emitter is sharp and the barrier is of a non-Fowler-Nordheim type, scaling the field does not necessarily lead to scaling of the current with d. Here we show that for d>>R it does.